17/3 : 7 = x : 7/38

To solve the proportion \( \frac{17/3}{7} = \frac{x}{7/38} \), we can use cross-multiplication. Cross-multiplying gives us: \[ (17/3) \times (7/38) = x \times 7 \] Now, calculate the left side: \[ \frac{17 \cdot 7}{3 \cdot 38} = \frac{119}{114} \] Now we have: \[ \frac{119}{114} = 7x \] To isolate \( x \), we can divide both sides by 7: \[ x = \frac{119}{114 \cdot 7} = \frac{119}{798} \] Therefore, the value of \( x \) is: \[ x = \frac{119}{798} \] If you want to simplify \( \frac{119}{798} \), you can divide both the numerator and the denominator by their greatest common divisor, which is 7: \[ x = \frac{119 \div 7}{798 \div 7} = \frac{17}{114} \] Thus, the final answer is: \[ x = \frac{17}{114} \]